Golf equipment fitting system and golf equipment fitting program

ABSTRACT

A golf equipment fitting system and a golf equipment fitting program is capable of providing accurate calculation results even when specifications that affect swing time are changed, and of outputting simulation results in a short period of time. 
     The golf equipment fitting system and the golf equipment fitting program calculate a swing response surface and a time response surface using a response surface methodology based on an obtained swing data. Also, the golf equipment fitting system and the golf equipment fitting program calculate the swing data of a golf club that is not used for measurement from the swing response surface and the time response surface, simulate a golf swing based on the calculated swing data, and output the results of simulations.

FIELD OF THE INVENTION

The present invention relates to a golf equipment fitting system and agolf equipment fitting program.

BACKGROUND ART

In 2008, restitution regulations on golf club heads were enacted by theRules of Golf, making it difficult to optimize distance by the headalone. In response to the regulations, manufacturers have switched theirfocus to the shaft and have attempted to improve carry by making themost of the bending of a shaft. Thus, as of 2012, varieties of shaftshave increased, resulting in a further increase in varieties of clubsderived from combinations of heads and shafts. Accordingly, when aplayer purchases a club, it is difficult for the player to select themost suitable equipment, especially the most suitable shaft for himself.

Fitting technologies are intended to solve the above problem. PatentPublication 1 discloses an example of a fitting technology that focuseson the entire golf club. The behavior of a head at the moment of impactis photographed by a high-speed camera, and the data are converted tothree-dimensional coordinates by a DLT method so that the position ofthe head is quantified. By so doing, the head position at the time ofimpact is specified for each club, enabling a golfer to choose a properclub. However, it is necessary for the golfer to use a large number ofclubs when actually hitting golf balls. Thus, even though a selection ofpreferable clubs is made available, it is still difficult for a golferto choose a club that is best suited to himself.

The technology described in Patent Publication 2 is meant to solve theabove problem. First, a golfer's swing is measured, and the headbehavior of a golf club is simulated based on the swing data. Byperforming only one swing measurement, the golfer can obtain a resultthat corresponds to hundreds of test hits. However, when a golfer usesclubs with different stiffnesses and weights, the golfer hits a ball bychanging the swing itself depending on the club. Thus, when the headbehavior is simulated on clubs or shafts with significantly differentproperties based on the data obtained by one swing, the simulationresults may not provide actual solutions.

The technology described in Patent Publication 3 is meant to solve theabove problem. Using response surface methodology, the technologycalculates swings which are different depending on shaft properties(three properties: flex, kick point, torque), and performs simulationsbased on the swing data modified accordingly. As a result, thetechnology provides simulations that are even closer to actualconditions.

PRIOR ART PUBLICATION Patent Publication

Patent Publication 1: JP2005-312734A

Patent Publication 2: JP4871218B

Patent Publication 3: JP2011-425A

SUMMARY OF THE INVENTION Problems to be Solved by the Invention

Using the technology described in Patent Publication 3, it is difficultto simulate by changing the “weights” and “lengths” of golf clubcomponents, for example. That is because when the weight or length ischanged, even for the same golfer, swing time differs significantly fromthe position at address (when a golf club is in contact with the ground)to the top (the moment the golf club is in full backswing), and from theposition at the top to impact (the moment the head touches the ball),and so forth, and sufficiently accurate calculation results cannot beobtained. Thus, the technology described in Patent Publication 3 islimited to being applied to golf club specifications excluding thosethat significantly affect swing time such as the weight or length of aclub.

In addition, it is difficult to instantly find appropriatespecifications from massive calculation results when the technology inPatent Publication 3 is used. Thus, it is difficult to apply thetechnology to a fitting system that requires instant feedback.

The present invention was carried out in consideration of the problemsabove. The objective is to provide a golf equipment fitting system and agolf equipment fitting program capable of providing accurate calculationresults even when specifications that affect swing time are changed, andof outputting simulation results in a short period of time.

Solutions to the Problems

In the following, numerical references as shown in the accompanyingdrawings are provided in parentheses for an easier understanding of thepresent invention. However, the present invention is not limited to theembodiments shown in the drawings.

To solve the aforementioned problems, an aspect of the present inventionis a golf equipment fitting system (2) provided with the following: aswing data acquisition unit (21) that acquires swing data from a sensorattached to multiple golf clubs with different specifications; a swingresponse surface computation unit (221) that calculates a swing responsesurface using the response surface methodology based on the swing dataobtained by the swing data acquisition unit; a time response surfacecomputation unit (222) that calculates a time response surface using theresponse surface methodology based on the swing data obtained by theswing data acquisition unit; a simulation unit (23) that calculates theswing data of a golf club that is not used for measurement from theswing response surface and the time response surface and simulates theswing of the golf club based on the obtained swing data; and a resultsoutput unit (24) that outputs the results of simulations conducted bythe simulation unit.

Another aspect of the present invention is characterized in that, in thegolf equipment fitting system, the specifications of multiple golf clubsto be used in simulations include at least the weight of a shaft.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the specifications of multiple golfclubs to be used in simulations include at least the length of a club.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the specifications of multiple golfclubs to be used in simulations include at least two differentspecifications, and the difference in impact degrees of the twodifferent specifications is within a predetermined value.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the specifications of multiple golfclubs to be used in simulations are nine specifications selected fromamong 27 specifications obtained in combination of three differentspecifications and three levels each of the three specifications basedon an L9 orthogonal array for the design of experiments.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the three different specificationsare weight, kick point and flex.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the three different specificationsare selected from among the stiffness, length, total weight and balanceof a club.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the three different specificationsare selected from among the height, depth, distance and angle of thecenter of gravity of the head.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the three different specificationsare the loft angle, lie angle and face angle of a club head.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, when the three differentspecifications are divided into their respective levels, and when thenumber of levels of a first specification is set as (i) and one level as(l), the number of levels of a second specification is set as (j) andone level as (m), and the number of levels of a third specification isset as (k) and one level as (n), the results output unit allocates aresult number defined by (l−1)i+(m−1)j+(n−1)k to each of the simulationresults, then, each result number is replaced with a plotted number,which is the value obtained by subtracting (j−1)×k×(l−1) from the resultnumber, and finally the results output unit outputs data as the fittingresults by entering the plotted numbers on the horizontal axis and thesimulation results on the vertical axis.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the results output unit outputs thefitting results as line segments by connecting the plotted dataapplicable to the following conditions (i)˜(iii):

-   -   (i) data in which a first specification is different from second        and third specifications while second and third specifications        are the same;    -   (ii) data in which a second specification is different from        first and third specifications while first and third        specifications are the same; and    -   (iii) data in which a third specification is different from        first and second specifications while first and second        specifications are the same.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the results output unit outputsfitting results by converting the results to a natural language inassociation with corresponding absolute values and inclinations.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the results output unit outputs aspecification that exhibits the maximum value in simulation results byconverting the specification to a product name.

Yet another aspect of the present invention is characterized in that, inthe golf equipment fitting system, the results output unit selects anddisplays a golf club based on the results of simulations conducted bythe simulation unit.

To solve the aforementioned problems, yet another aspect of the presentinvention is a golf equipment fitting program including the followingsteps that are implemented by a computer: a swing data acquisition stepto acquire swing data by attaching a sensor to multiple golf clubs withdifferent specifications; a swing response surface computation step tocalculate a swing response surface using the response surfacemethodology based on the swing data obtained by the swing dataacquisition step; a time response surface computation step to calculatea time response surface using the response surface methodology based onthe swing data obtained by the swing data acquisition step; a simulationstep to calculate the swing data of a golf club that is not used formeasurement from the swing response surface and the time responsesurface and to simulate the swing of the golf club based on the obtainedswing; and a results outputting step to output the results ofsimulations conducted by the simulation step.

Effects of the Invention

According to the present invention, even when specifications that mayaffect swing time are changed, accurate computation results are obtainedand simulation results are outputted in a short period of time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a diagram showing the structure of a first embodiment ofthe present invention;

FIG. 2 shows views illustrating examples of specifications of a golfshaft;

FIG. 3 shows views illustrating examples of specifications of a golfshaft and club heads;

FIG. 4 is a table showing specifications of nine golf clubs for testhitting to obtain swing data;

FIG. 5 shows a flowchart showing operations of the golf equipmentfitting system 2 shown in FIG. 1;

FIG. 6 is a graph showing swing data when shaft weights are the same;

FIG. 7 is a graph showing swing data when shaft weights are different;

FIG. 8 is a graph showing swing data prepared using only a swingresponse surface;

FIG. 9 is a graph showing swing data prepared using both a swingresponse surface and a time response surface;

FIG. 10 is a graph showing simulation results without applying aspecific process;

FIG. 11 is a table showing relationships of simulation numbers andspecifications of golf clubs;

FIG. 12 is a table showing relationships of result numbers andspecifications of golf clubs after result numbers are assigned;

FIG. 13 is a graph showing simulation results obtained by enteringresult numbers on the horizontal axis;

FIG. 14 is a graph showing simulation results obtained by enteringplotted numbers on the horizontal axis;

FIG. 15 is a table schematically showing nine different trajectories;

FIG. 16 is a graph showing simulation results obtained by entering the Fvalues as complex conditions on the vertical axis;

FIG. 17 is a table showing impact degrees of specifications; and

FIG. 18 is a graph showing the results of simulations conducted byselecting the head weight, torsional rigidity distribution of a shaftand height of the center of gravity of a head as three differentspecifications.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following, a golf equipment fitting system is described accordingto an embodiment of the present invention by referring to theaccompanying drawings. Here, golf shaft specifications are listed asspecification examples of golf equipment, but they are not the onlyoptions. FIG. 1 is a diagram showing the structure of the presentembodiment. In the drawing, numerical reference 1 indicates a golf clubwhere a golf shaft with known specifications is attached thereon, and isprovided with sensor 11 inserted in the grip section of the shaft, andtransmitter 12 that transmits the output signal from sensor 11 to theoutside through wireless communication. Sensor 11 may be installedoutside the shaft. Sensor 11 is a 6-axis sensor that detects and outputs3-axis acceleration and 3-axis angular velocity. Sensor 11 may also be a9-axis sensor to measure 3-axis orientations using geomagnetism inaddition to 3-axis acceleration and 3-axis angular velocity.Alternatively, a 6-axis sensor and 3-axis geomagnetism sensor may beused together as sensor 11.

Numerical reference 2 is a golf equipment fitting system using acomputer. Numerical reference 20 is a receiver unit that receives dataoutputted by sensor 11 (swing data) transmitted by transmitter 12.Numerical reference 21 is a swing data acquisition unit that acquiresswing data through receiver unit 20. Numerical reference 221 is a swingresponse surface computation unit which calculates a swing responsesurface based on the swing data when a golf club 1 is test hit.Numerical reference 222 is a time response surface computation unitwhich calculates a swing time response surface based on the swing datawhen a golf club 1 is test hit. Numerical reference 23 is a simulationunit which conducts simulations by FEM (Finite Element Method) using theswing response surface and time response surface. Numerical reference 24is a results output unit which outputs the results of simulationsconducted in simulation unit 23.

Next, a golf club 1 is described. Golf club 1 is used for test hittingto obtain swing measurement data. When a golfer swings a club, thegolfer adjusts the swing according to club properties such as the shaftweight, flexural rigidity and torsional rigidity. Thus, if swingmeasurement data are obtained for analysis by using a golf club withspecific properties, it is difficult to achieve proper analysis results.That is because swings differ depending on club specifications. Thus,based on the design of experiments, three different specifications areselected from numerous club specifications, and 27 golf clubs areprepared by applying three levels each to the three specifications.Among the 27 golf clubs, nine clubs are selected based on the L9orthogonal array. To obtain 3-factor and 3-level data without using thedesign of experiments, it is necessary to conduct experiments on 3³=27golf clubs, and such procedures are not practical. Here, as examples ofspecifications, the following are picked: the weight of a shaft, theflexural rigidity of a shaft (among shaft specifications corresponds tothe flex, hereinafter referred to as “flex”), and the flexural rigiditydistribution of the shaft (among shaft specifications corresponds tokick points, hereinafter referred to as “kick point”). Threespecifications of a golf club to be used here each have three levels.However, they are not the only options, and any other clubs may be usedas long as they have multiple different specifications. The presentembodiment is preferably applied to golf clubs with specifications ofdifferent weights and lengths.

As shown in FIG. 2, three specifications of a shaft selected in theexample are the weight of the shaft only, the flex specified by thedegree of deflection (FIG. 2( a)), and the kick point specified bycoefficient (C) of function (P), indicating the point of maximum bendingof the shaft (FIG. 2( b)).

FIG. 2( a) shows an example where a position 920 mm from the tip end ofa shaft is supported from below, a position 150 mm further from thatpoint toward the butt end (1070 mm from the tip end) is supported fromabove, and a load of 3.0 kgf is exerted on a position 10 mm from the tipend. The value of displacement at the tip end indicates the flex(flexural rigidity).

FIG. 2( b) shows examples of kick points (flexural rigidity distributionL (x)). In the graph, “EI (i)” indicates flexural rigidity, and “x”indicates a position on the shaft based on the tip end of the shaft.Flexural rigidity distribution L(x) is represented by a formulaL(x)=C0×P0(x)+C1×P1(x)+C2×P2(x)+C3×P3(x) . . . .

Regarding the point of maximum bending of a shaft, kick points aresorted into a high kick point positioned closer to the grip, a low kickpoint positioned closer to the head, and a middle kick point positionedin between.

Kick points are categorized as high, low or middle kick points accordingto the value specified by coefficient (C) of function (P). Swing dataare obtained by using one of the aforementioned nine golf clubs 1.

Examples of other specifications applicable to the system are torsionalrigidity of a shaft (corresponds to the torque among shaftspecifications, hereinafter referred to as “torque”), torsional rigiditydistribution of a shaft, shaft weight distribution, golf club length,head weight, club balance, the depth, height and distance of the centerof gravity of the head, grip weight, loft angle, lie angle, and faceangle.

As shown in FIG. 3, the torque is determined by the torsional angle of ashaft. FIG. 3( a) shows an example where a point 1035 mm from the tipend of a shaft is fixed and a torsional rigidity load is exerted on apoint 45 mm from the tip of the shaft. Here, (A) is set rotatable whilefixed in a direction of bending, and (B) is entirely fixed. In addition,a torsional load of 1.152 kgf is exerted at a point 120 mm from theshaft axis. The torsional angle at the tip end of the shaft obtainedabove is defined as the torque.

The depth of the center of gravity of the head is specified as the depth(distance) from the face to the center of gravity of a head (FIG. 3(b)). The height of the center of gravity of the head is specified as thelength from the leading edge to the center of gravity on the face, andthe distance is specified as the length obtained by extending aperpendicular line from the shaft axis toward the center of gravity onthe face (FIG. 3( c)). The torsional rigidity distribution and weightdistribution of a shaft are described the same as the relationship ofthe flexural rigidity distribution and kick points.

Club balance (also referred to as swing weight) indicates the feel ofthe head weight (meaning how the weight of the head feels during a swingor waggle). Club balance is measured by a club balance scale, “Golf ClubScale,” made by Kenneth Smith Inc.

The club stiffness is indicated by the frequency of vibration with agrip and head attached thereon. The frequency of vibration is measuredby a “Golf Club Timing Harmonizer” made by Fujikura Rubber Ltd. Forexample, the stiffness of a club is specified as the number ofvibrations per minute obtained at a point 760 mm from the grip end whenthe club vibrates while a point 180 mm from the grip end is fixed.

FIG. 4 shows specifications of nine golf clubs for test hitting toobtain swing data based on the L9 orthogonal array in experimentaldesign. Shaft weights show normalized values; the smaller valueindicates a greater weight. In addition, flex values are normalized; thesmaller value indicates higher rigidity. Shaft weight and flex are bothset in a range applicable for a golf shaft when the shaft has a normallength and diameter. Here, regarding the shaft weight, if the level isindicated as “0,” the shaft weight is specified as 80 g, if it is “0.5,”the weight is 70 g, and if it is “1,” the weight is 60 g. Regarding theflex, if the level is indicated as “0,” the value of flex (flexuralrigidity) is 130 mm, if it is “0.5,” the value is 180 mm, and if it is“1,” the value is 220 mm. Regarding the kick point, if the level isindicated as “0,” it is a low kick point; if it is “0.5,” it is a middlekick point; and if it is “1,” it is a high kick point. The number ofclubs is not limited to nine, and any other number may be tested as longas practical experiments can be conducted.

The heads attached to the golf clubs shown in FIG. 4 are the same, andthe shaft length and the weight of each golf club are also the same.Except for the specifications to be analyzed in a fitting process, therest of the specifications are set the same so that other factors areeliminated from causing variations during the fitting process. Inaddition, when sensor 11, transmitter 12 and the like are inserted inthe shaft, the total weight of sensor 11, transmitter 12 and devicesnecessary to drive them is set within 20 grams so as to avoid anincrease in the entire weight of a golf club 1. Accordingly, by using acommercially available lightweight grip, an increase in the entireweight is suppressed. Thus, negative impacts caused on the swing by anincrease in club weight are suppressed.

Next, procedures of golf equipment fitting system 2 shown in FIG. 1 aredescribed with reference to FIG. 5. First, among nine golf clubs 1, aperson who performs test hitting (a user: fitting subject) uses a golfclub 1 with club No. 1. Sensor 11 outputs the detected results obtainedduring the test hitting (swing data) to transmitter 12. Transmitter 12receives the swing data outputted from sensor 11, and transmits theswing data to the outside of the shaft through wireless communication.Receiver 20 receives the swing data and outputs the data to swing dataacquisition unit 21. Swing data acquisition unit 21 retains the swingdata (step S1).

The above procedure is repeated on other golf clubs 1 (club Nos. 2˜9)and swing data acquisition unit 21 retains chronological swing dataobtained when the user has conducted at least one test hit on each ofnine golf clubs 1. Swing data acquisition unit 21 converts the swingdata to moving velocity data of the grip portion of a golf club 1 andthe axial rotation data of the shaft. Such conversions are obtained bygeometrically calculating the positional relationship between theposition of sensor 11 inserted in a golf club 1 and the two pointsdetermined in advance on the grip portion of a golf club 1.

In the present embodiment, from the total swing data acquired, swingdata acquisition unit 21 converts only the swing data obtained from theposition at the top (when the club is in full backswing) to the positionat impact (when the head strikes the ball) into moving velocity data andaxial rotation data. However, it is an option to set the subject foranalysis to be the swing data obtained from address (when the golf clubis in contact with the ground) to impact.

Next, swing response surface computation unit 221 reads out the swingdata of the nine clubs retained in swing data acquisition unit 21 andcalculates a response surface by putting the skills and habits of theuser expressed in a linear function (step S2). A swing response surfaceindicates a relational expression among moving velocity data of the gripportion and axial rotation data obtained during test hitting of the ninegolf clubs shown in FIG. 4 and three specifications (shaft weight, flex,kick point) of the golf club.

Formula 1 is as follows. Swing data obtained by multiple golf clubs arerepresented by f₁˜f₉, and time (t) is discretized into t={t₁, . . . ,t_(n)}. Since nine golf clubs are used for test hitting in the presentembodiment, swing data is set as f₁˜f₉. However, the values differdepending on the number of test clubs. Moreover, f_(j)(t_(i)) is themeasurement value obtained by test hitting No. “j” golf club, morespecifically, values of 3-axis acceleration {a_(x), a_(y), a_(z)} and3-axis angular velocity (ω_(x), ω_(y), ω_(z)).

When three specifications (design parameters) of the nine golf clubs areset as {x_(j), y_(j), z_(j)} (j=1˜9), the relationship represented informula 1 is obtained. Then, to each “t_(i)”, formula 1 is used toobtain solutions.

Here, “x, y, z” are design parameters: “x” is a first specification(shaft weight), “y” is a second specification (flex) and “z” is a thirdspecification (kick point). Numbers “1˜n” in “x₁˜x_(n)”, “y₁˜y_(n)” and“z₁˜z_(n)” correspond to the club numbers. In addition, any convenientvalue for analysis is assigned to each of x bar, y bar and z bar (suchas intermediate values of design parameters).

$\begin{matrix}{\begin{Bmatrix}{f_{1}\left( t_{i} \right)} \\{f_{2}\left( t_{i} \right)} \\\; \\{f_{9}\left( t_{i} \right)}\end{Bmatrix} = {\begin{bmatrix}1 & \left( {x_{1} - \overset{\_}{x}} \right) & \left( {y_{1} - \overset{\_}{y}} \right) & \left( {z_{1} - \overset{\_}{z}} \right) \\1 & \left( {x_{2} - \overset{\_}{x}} \right) & \left( {y_{2} - \overset{\_}{y}} \right) & \left( {z_{2} - \overset{\_}{z}} \right) \\\; & \; & \; & \; \\1 & \left( {x_{9} - \overset{\_}{x}} \right) & \left( {y_{9} - \overset{\_}{y}} \right) & \left( {z_{9} - \overset{\_}{z}} \right)\end{bmatrix}\begin{Bmatrix}{a_{1}\left( t_{i} \right)} \\{a_{2}\left( t_{i} \right)} \\{a_{3}\left( t_{i} \right)} \\{a_{4}\left( t_{i} \right)}\end{Bmatrix}}} & \left\lbrack {{formula}\mspace{14mu} 1} \right\rbrack\end{matrix}$

By solving formula 1, coefficients “a₁˜a₄” of the response surface areobtained as expressed by formula 2. When n=5 or greater, formula 1 istypically in excessive conditions, and there is no exact solutionavailable. Thus, a generalized inverse matrix A+ (also referred to as aMoore-Penrose inverse matrix or pseudo-inverse matrix) is used. That isthe method for calculating an approximate value when no exact solutionis available. Namely, it is a method for obtaining the minimum value oferror |Ax−b|². Since it is a common mathematical method, a detaileddescription is omitted here. Technical computing software “MATLAB,” madeby MathWorks Inc., is used to solve formula 1.

Coefficients “a₁˜a₄” obtained by using formula 2 are the valuescorresponding to the skills and swing habits of the test hitter. Namely,even when “x, y, z” are changed to specifications that are not measured,swing data represented by function “f” as shown in formula 3 will beobtained. In other words, formula 3 provides approximate values of3-axis acceleration and 3-axis angular velocity for any parameters {x,y, z}. From formula 3, swing data for No. “m” golf shaft that has notbeen measured are represented by formula 4. The f_(m)(t) is a swingresponse surface obtained by formula 4.

$\begin{matrix}{\begin{Bmatrix}{a_{1}\left( t_{i} \right)} \\{a_{2}\left( t_{i} \right)} \\{a_{3}\left( t_{i} \right)} \\{a_{4}\left( t_{i} \right)}\end{Bmatrix} = {A^{+}\begin{Bmatrix}{f_{1}\left( t_{i} \right)} \\{f_{2}\left( t_{i} \right)} \\\; \\{f_{9}\left( t_{i} \right)}\end{Bmatrix}}} & \left\lbrack {{formula}\mspace{14mu} 2} \right\rbrack \\{{f\left( t_{i} \right)} = {{a_{1}\left( t_{i} \right)} + {{a_{2}\left( t_{i} \right)}\left( {x - \overset{\_}{x}} \right)} + {{a_{3}\left( t_{i} \right)}\left( {y - \overset{\_}{y}} \right)} + {{a_{4}\left( t_{i} \right)}\left( {z - \overset{\_}{z}} \right)}}} & \left\lbrack {{formula}\mspace{14mu} 3} \right\rbrack \\{{f_{m}(t)} = {{a_{1}(t)} + {{a_{2}(t)}\left( {x_{m} - \overset{\_}{x}} \right)} + {{a_{3}(t)}\left( {y_{m} - \overset{\_}{y}} \right)} + {{a_{4}(t)}\left( {z_{m} - \overset{\_}{z}} \right)}}} & \left\lbrack {{formula}\mspace{14mu} 4} \right\rbrack\end{matrix}$

When the swing time varies depending on the golf club and when a swingtime for a golf club is set at “t_(k)” (k=1, . . . , 9), the samplingtime is normalized for a club “k” as represented by formula 5.

$\begin{matrix}{t_{i} = {\frac{i}{n}t_{k}}} & \left\lbrack {{formula}\mspace{14mu} 5} \right\rbrack\end{matrix}$

If no significant variation is observed in swing time, the shortestswing time “t_(min)” among nine clubs may be employed so that thenormalization process is omitted.

Next, time response surface computation unit 222 reads out the swingdata of nine clubs retained in swing data acquisition unit 21 andcalculates a time response surface with a normalized swing time of thetest hitter (step S3). A time response surface means a relationalexpression among three specifications (here, shaft weight, flex and kickpoint of a golf club) and swing times obtained when nine golf clubsshown in FIG. 4 were used for test hitting. A time response surface iscalculated by using formulas 6˜8.

In formula 6, “g₁˜g₉” indicate swing times of nine golf clubsrespectively, and coefficients “b₁˜b₄” obtained by formula 7 correspondto swing times of the test hitter. By conducting those calculations, thedifference in swing times caused by a difference in weights is obtained.

$\begin{matrix}{\begin{Bmatrix}g_{1} \\g_{2} \\\; \\g_{9}\end{Bmatrix} = {\begin{bmatrix}1 & \left( {x_{1} - \overset{\_}{x}} \right) & \left( {y_{1} - \overset{\_}{y}} \right) & \left( {z_{1} - \overset{\_}{z}} \right) \\1 & \left( {x_{2} - \overset{\_}{x}} \right) & \left( {y_{2} - \overset{\_}{y}} \right) & \left( {z_{2} - \overset{\_}{z}} \right) \\\; & \; & \; & \; \\1 & \left( {x_{9} - \overset{\_}{x}} \right) & \left( {y_{9} - \overset{\_}{y}} \right) & \left( {z_{9\vdots} - \overset{\_}{z}} \right)\end{bmatrix}\begin{Bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{Bmatrix}}} & \left\lbrack {{formula}\mspace{14mu} 6} \right\rbrack \\{\begin{Bmatrix}b_{1} \\b_{2} \\b_{3} \\b_{4}\end{Bmatrix} = {B^{+}\begin{Bmatrix}g_{1} \\g_{2} \\\; \\g_{9}\end{Bmatrix}}} & \left\lbrack {{formula}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Next, each “t” is converted to “g_(m)” based on formula 8. A timeresponse surface is obtained when “g_(m)” is calculated by formula 8.Also, “f_(m)′(t)” is calculated by formula 9 to provide new swing databased on the swing response surface and the time response surface.

$\begin{matrix}{g_{m} = {b_{1} + {b_{2}\left( {x_{m} - \overset{\_}{x}} \right)} + {b_{3}\left( {y_{m} - \overset{\_}{y}} \right)} + {b_{4}\left( {z_{m} - \overset{\_}{z}} \right)}}} & \left\lbrack {{formula}\mspace{14mu} 8} \right\rbrack \\{{f_{m}^{\prime}(t)} = {f_{m}\left( {\frac{g_{m}}{t_{i}n}t} \right)}} & \left\lbrack {{formula}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Then, the swing data of a golf club that is not used for measurement iscalculated by simulation unit 23 based on the moving velocity data andaxial rotation data of the grip portion that were measured and retainedin swing data acquisition unit 21, the swing response surface calculatedby swing response surface computation unit 221 and the time responsesurface calculated by time response surface computation unit 222. Basedon the calculated swing data, simulation unit 23 simulates the movementof a club head using a dynamic finite element method (step S4).

The simulation results showing the movement of a golf club obtained bythe above analysis are the club speed at the time of impact, face angle(horizontal angle of the club face relative to the flight line of theball), and impact loft (loft angle relative to the ground at the time ofimpact). The club speed corresponds to the carry of the ball, the faceangle corresponds to the direction of the ball, and the impact loftcorresponds to the height of trajectory. Other than those listed above,the simulation results may be obtained on any other values, for example,club path, attack angle, ball speed, carry and the like.

The analysis of the movement of a club head using a dynamic finiteelement method is conducted by a known method (a commercially availablesoftware for finite element analysis, for example); a detaileddescription is omitted here. Simulation unit 23 analyzes the movement ofa club head by using all the possible specifications of a golf club andby inputting a swing response surface in which the skills and habits ofthe test hitter are expressed in a linear function and a time responsesurface in which swing time of the test hitter is normalized.Accordingly, the movement of another golf club is simulated, reflectingthe skills, habits and swing time of the test hitter (variations inswing characteristics and swing time using a golf club with differentspecifications).

As described above, the weight and length of a golf club havesignificant impact on the swing time. FIGS. 6 and 7 show examples ofswing data respectively when shaft weights are the same (FIG. 6) andwhen shaft weights are different (FIG. 7) (ω_(x), for example). Whenshaft weights are the same, swing times show fewer variations as shownin FIG. 6. On the other hand, when shaft weights differ from each other,for example, 40 g, 60 g and 80 g, swing times vary significantly asshown in FIG. 7.

To solve formula 2 by using a generalized inverse matrix in the abovesituation, “t” is necessary to be set constant. When swing times do notvary as shown in FIG. 6, no significant error will result when a swingtime is set constant by any method. However, when swing times varynotably as shown in FIG. 7, a significantly large error will be causedif swing time is set constant. Thus, time response surface computationunit 222 calculates a time response surface after each “t” isnormalized. Then, when “t” is converted again based on the obtained timeresponse surface, swing time data reflecting the swing time areachieved.

As described above, even when weight and length factors are changed,swing data that reflect a proper swing time are achieved. Thus, accuratesimulation results are achieved even on specifications such as weightand length that have significant impact on the swing time. Strictlyspeaking, swing times also vary on specifications that do not have muchimpact on the swing time. By introducing a swing response surface and atime response surface, calculation accuracy is improved even onspecifications having little impact on swing time. FIG. 8 shows datacalculated using only a swing response surface, and FIG. 9 shows datacalculated using both swing response surface and time response surface.

Next, a description is provided for the procedures to create result datato be outputted by results output unit 24. Here, regarding thespecifications of a shaft to be analyzed, the number of levels of shaftweight (number of levels “i” into which a first specification isdivided) is 3, the number of levels of flex (number of levels “j” intowhich a second specification is divided) is 5, and the number of levelsof kick point (number of levels “k” into which a third specification isdivided) is 5. The number of levels indicates any selected number oflevels for the specifications of nine clubs actually used for testhitting. For example, regarding flex, there are “X, R, L” levelsobtained when nine clubs are actually test hit; when the number oflevels “j” into which flex is divided is set at 5, two more levels,namely, “S, A” are added to express levels between the three levels (thelevels of flex are expressed as “X, S, R, A, L” in order from thestiffest.)

In the above situation, simulation unit 23 obtains simulation results onthe movements of golf clubs equipped with 3×5×5=75 shafts. When theresult data are outputted for display by entering club speeds on thevertical axis and simulation numbers on the horizontal axis, the displaywill be as shown in FIG. 10. It is difficult to grasp from FIG. 10 whichdot indicates a shaft having a certain specification value. FIG. 11shows relationships between simulation numbers and club specifications.

Therefore, the following procedure allows a user to find the values ofshaft specifications.

First, a result number is allotted to each simulation number based onthe following definition. When the number of levels into which a firstspecification is divided is set as “i” and one level as “1”, the numberof levels into which a second specification is divided is set as “j” andone level as “m”, and the number of levels into which a thirdspecification is divided is set as “k” and one level as “n”, then theresult number is obtained by (l−1)i+(m−1)j+(n−1)k. In other words, theprocess is conducted by the following steps.

[1] Setting the lowest level for each of the first and secondspecifications, the level of the third specification is changed from thelowest to the highest;

[2] Setting the lowest level for the first specification and setting onelevel higher for the second specification, the level for the thirdspecification is changed from the lowest to the highest;

[3] Step [2] is repeated until the process is conducted for the highestlevel of the second specification;

[4] Setting one level higher for the first specification, [2] and [3]are conducted; and

[5] Step [4] is repeated until the process is conducted for the highestlevel of the first specification.

The above procedures are described in detail below:

(A) The shaft weight is fixed to the first level, the flex is fixed tothe first level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(B) The shaft weight is fixed to the first level, the flex is fixed tothe second level, and the kick point is changed on 5 levels from lowkick point toward high kick point;

(C) The shaft weight is fixed to the first level, the flex is fixed tothe third level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(D) The shaft weight is fixed to the first level, the flex is fixed tothe fourth level, and the kick point is changed on 5 levels from lowkick point toward high kick point;

(E) The shaft weight is fixed to the first level, the flex is fixed tothe fifth level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(F) The shaft weight is fixed to the second level, the flex is fixed tothe first level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(G) The shaft weight is fixed to the second level, the flex is fixed tothe second level, and the kick point is changed on 5 levels from lowkick point toward high kick point;

(H) The shaft weight is fixed to the second level, the flex is fixed tothe third level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(I) The shaft weight is fixed to the second level, the flex is fixed tothe fourth level, and the kick point is changed on 5 levels from lowkick point toward high kick point;

(J) The shaft weight is fixed to the second level, the flex is fixed tothe fifth level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(K) The shaft weight is fixed to the third level, the flex is fixed tothe first level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(L) The shaft weight is fixed to the third level, the flex is fixed tothe second level, and the kick point is changed on 5 levels from lowkick point toward high kick point;

(M) The shaft weight is fixed to the third level, the flex is fixed tothe third level, and the kick point is changed on 5 levels from low kickpoint toward high kick point;

(N) The shaft weight is fixed to the third level, the flex is fixed tothe fourth level, and the kick point is changed on 5 levels from lowkick point toward high kick point; and

(O) The shaft weight is fixed to the third level, the flex is fixed tothe fifth level, and the kick point is changed on 5 levels from low kickpoint toward high kick point.

When result numbers are defined in the order of (A)˜(O) above, resultnumbers are determined as shown in FIG. 12. In FIG. 12, the shaft weight“0” means the shaft is heavy (80 g, for example), the shaft weight “0.5”means the shaft is midweight (70 g, for example), and the shaft weight“1” means the shaft is lightweight (60 g, for example). Also, flex “0”means the shaft is stiffest (for example, flex “X”), and as the valueincreases from flex “0.25” (for example, flex “S”), “0.5” (for example,flex “R”) to the “0.75” (for example, flex “A”), it means the shaft isgradually more flexible. Flex “1” indicates the most flexible shaft (forexample, flex “L”). Kick point “0” indicates a low kick point, kickpoint “0.25” indicates a low-mid kick point, kick point “0.5” indicatesa middle kick point, kick point “0.75” indicates a mid-high kick point,and kick point “1” indicates a high kick point.

Based on the above, when the obtained values are plotted by enteringclub speeds on the vertical axis and result numbers on the horizontalaxis, FIG. 13 shows the results. When simulation unit 23 conductssimulations in a certain order, and when results output unit 24 outputsthe results based on that order, club speed trends are forecast as shownin FIG. 13. However, the outputted pattern as shown in FIG. 13 is stillinsufficient to provide an easy grasp of the trend.

Results output unit 24 subtracts (j−1)×k×(l−1) from the result numbersand plots again the obtained values as plotted numbers. FIG. 14 showsfitting results which are obtained by plotting values as above and areoutputted accordingly.

More specifically, results output unit 24 assigns plotted numbers byconverting result numbers as (a)˜(d) below, and outputs the resultsagain by entering the plotted numbers and simulation results, allowingthe user to grasp the relationship trend between the specificationvalues of golf equipment and the simulation results.

(a) The results obtained in simulations (A)˜(E) are plotted;

(b) The results obtained in simulations (F)˜(J) are plotted by shiftingthe values to the left. The value to be shifted is 20 points on the axis“x” (=75/3−5=20);

(c) The results obtained in simulations (K)˜(O) are plotted by shiftingthe same as above from the values plotted in (b); and

(d) Those that show a difference only in kick points, those that show adifference only in flex levels, and those that show a difference only inshaft weights are connected respectively by straight lines.

To avoid complexity, all kick points are connected, whereas flex levelsand shaft weights are connected only at their respective end values ofspecifications. Here, actual simulation result values are connected bystraight lines, but it is an option to approximate points connected bystraight lines using a quartic function and to use the obtainedapproximate values as simulation result values. By using a quarticfunction approximation method, variations in swings that are likely tooccur in a novice golfer are absorbed, and more meaningful results areachieved.

In FIG. 14, the vertical axis shows club speed; a greater valueindicates a faster speed (long carry), and a smaller value indicates aslower speed (short carry). The horizontal axis shows newly assignedplotted numbers. In FIG. 14, the mark indicates a golf club that isassociated with a specification. Each value is associated with a valueof “flex,” “kick point” or “shaft weight,” which are specifications ofthe golf shaft.

From the examples of output results shown in FIG. 14, it is found that ashaft weight of “60 g,” stiffest flex “X” and “mid-high kick point”should be selected to achieve maximum speed. Here, club speed is shownas an example. However, face angle, impact loft and the like are alsodisplayed by using the same method.

Moreover, results output unit 24 may display the trend of specificationsby using a natural language. Namely, results output unit 24 may displaythe fitting results by converting the results into a natural language inassociation with the corresponding absolute value and inclination foreach result. For example, if the purpose of fitting is to increase clubspeed, results output unit 24 displays “club speed will increase if theflex is stiffer,” “club speed will increase if the shaft is lighter,”“club speed will increase if the kick point is high,” “the impact fromthe shaft weight is greatest,” and the like. If the purpose of fittingis to improve the ball flight by increasing the impact loft, resultsoutput unit 24 displays “the ball flight is higher if the flex isstiffer,” “the ball flight is higher if the shaft is lighter,” “the ballflight is higher if the kick point is low,” “the impact of the flex isgreatest” and the like. Accordingly, it makes it easier for a user tograsp the trend of specifications by a natural language and to selectgolf equipment more easily.

Since “club speed” as the purpose of fitting is associated withspecifications when the results are outputted, the association withspecifications is obtained at a glance. In addition, results output unit24 is set not only to output the specification of a shaft that exhibitsthe maximum club speed but also to output all the availablespecifications. Accordingly, a user can select such specifications thatallow the user to achieve a moderate carry, a moderate trajectoryheight, and a moderate trajectory curve. That is especially effectivewhen face angles are calculated, since it is preferable for the user toselect a shaft that exhibits a moderate trajectory curve. When a userintends to produce a trajectory curve and if the user chooses a shaftthat causes a maximum curve, the user may face an excessive trajectorycurve.

FIG. 14 shows examples where results output unit 24 displays informationusing characters associated with specifications. However, relatedspecifications may also be displayed in different colors. To make thedisplay easier to grasp, results output unit 24 may output the resultsby changing the color density of the lines or the like so that thoseincluding the best values will stand out. Moreover, as furthersimplified data of those shown in FIG. 14, results output unit 24 mayoutput another communication method that replaces a natural language.

In the above descriptions, the shaft weight (3 levels) is set as a firstspecification, the flex (5 levels) is set as a second specification, andthe kick point (5 levels) is set as a third specification. However, thatis not the only option.

For example, it is an option to set the torque (5 levels) as a firstspecification, the flex (5 levels) as a second specification, and thekick point (5 levels) as a third specification. Alternatively, it isanother option to set the flex (5 levels) as a first specification, thetorque (5 levels) as a second specification, and the shaft weight (3levels) as a third specification.

Next, procedures are described to output complex conditions such as clubspeed and trajectory height, or club speed and trajectory curve, asfitting results. Generally, a golfer requires for a golf club not asingle performance but complex performances; for example, preventingslice, while maximizing club speed and simultaneously increasingtrajectory height, or the like. When complex conditions are outputted,one of the nine trajectories shown in FIG. 15 is selected by a user. Thetrajectory of a ball is determined by the height and direction of thetrajectory. When trajectory height is sorted into “High” (hightrajectory), “Mid” (medium trajectory) and “Low” (low trajectory), andthe trajectory direction is sorted into “Fade,” “Straight” and “Draw,”nine combinations are obtained as shown in FIG. 15. Here, “Fade” meansthe trajectory curves to the right when a user is right-handed, and“Draw” means the trajectory curves to the left when a user isright-handed. Then, results output unit 24 outputs conditions thatsatisfy the selected trajectory while the club speed is maximized. Tooutput complex conditions, specifications that maximize a targetfunction (F) are selected. Target function (F) is expressed in“F=a×f₁+β×f₂+γ×f₃.”

In the above formula, “f₁” represents first result data (club speed, forexample), “f₂” represents second result data (face angle, for example),“f₃” represents third result data (impact loft, for example), and “α, β,γ” are each a weight coefficient. Here, “α, β, γ” are selected properlyaccording to the choice made by a user. Generally, “α” is preferred tobe 1˜3 times the value of “β+γ.” That is because club speed is mostimportant for a golfer.

FIG. 16 shows examples of fitting results when a Low/Draw trajectory andmaximum club speed are set as complex conditions. Here, the verticalaxis shows which shaft is the best to hit a Low/Draw trajectory whileincreasing club speed. From the graph, the best specifications for theuser are the shaft weight of 60 g, flex of “S” and middle kick point.

Results output unit 24 may display the specification that shows themaximum simulation results (club speed, impact loft, face angle and thelike) by converting the results into actual product names of golfequipment.

As described, by selecting a trajectory, a user can select a shaft mostpreferable to achieve the selected trajectory. Accordingly, the user caneasily select the golf equipment most suitable to achieve desiredtrajectory. Namely, golf equipment fitting is conducted by theaforementioned golf equipment fitting system. The system is capable ofconducting measurement and analysis, and displaying the results in ashort period of time. Accordingly, the system provides a user withvisual determination for specifications of the most suitable golf shaft.

In the example above, the shaft weight, flex and kick point are selectedas factors. However, that is not the only option. Also, factors are notlimited to 3 specifications, and more or fewer specifications may beselected. As described above, it is preferred to select specificationsthat may affect swing time (shaft weight and club length, for example).Other specifications to be selected are the flexural rigidity, torsionalrigidity, weight, flexural rigidity distribution, torsional rigiditydistribution and weight distribution of a shaft; the length of a golfclub; head weight; club balance; the depth, height and distance of thecenter of gravity of the head; grip weight; loft angle, lie angle andface angle.

As for a time response surface, the data with the longest swing time maybe used so as to set all the swing times to be equal. In such a case,moderate accuracy and shortened calculation time are achieved.

When multiple different specifications are selected, it is preferred toselect a combination of those having similar impact degrees. An impactdegree means the degree of impact on the final behavior of the head whencertain specifications are changed. FIG. 17 shows degrees of impact. Thereasons are as follows.

FIG. 18 shows the result of simulations when three differentspecifications are as follows: head weight (impact degree: 5), torsionalrigidity distribution of a shaft (impact degree: 1), and height of thecenter of gravity of the head (impact degree: 1). When specificationshave impact degrees significantly different from each other, theobtained data mostly display the specifications with a greater impactdegree, and the results of the rest with smaller impact degrees are hardto read. Thus, it is preferred to select specifications having impactdegrees within a certain range (in the present embodiment, within 2).Also, the impact degrees of three different specifications are morepreferred to be the same. In the example shown in FIG. 18, it is foundthat head speed varies depending on the head weight, but no differenceis found in the two other specifications.

When three specifications are combined, it is preferred to use shaftweight, flexural rigidity (flex) and flexural rigidity distribution(kick point). In such a combination, the results are preferably used forfitting and designing shafts.

In addition, flexural rigidity (flex), club length and head weight maybe combined. In such a combination, the results are preferably used forfitting and designing clubs.

Moreover, the height, depth, distance and angle of the center of gravityof the head may be combined. In such a combination, the results arepreferably used for fitting and designing heads.

Furthermore, the loft angle, lie angle and face angle of a head may becombined. In such a combination, the results are preferably used forfitting and designing heads. Also, the stiffness, length, total weightand balance of a club may be combined.

Preferred combinations are listed above. However, they are not the onlyoptions.

The program for executing functions of the golf equipment fitting systemmay be recorded on a computer readable memory medium, and a computersystem may read out the stored program on the medium and execute theprogram. Here, “a computer system reads out the stored program on arecording medium and executes the program” includes installing theprogram in a computer system. Here, a “computer system” includes the OSand hardware such as peripheral devices. Also, a “computer system” mayinclude multiple computer devices connected through the Internet, WAN,LAN and networks that include exclusive communication lines. “Computerreadable recording media” means portable media such as flexible disks,magneto-optical disks, ROM and CD-ROM, and recording devices such ashard discs built into a computer system. The recording medium to storethe program may be a non-transitory recoding medium such as a CD-ROM.Also, a recording medium includes a memory medium installed internallyor externally to be accessible for a distribution server to distributethe program. The code stored in the recording medium of the distributionserver may be different from the code that allows the terminal device toexecute the program. Namely, the memory code to be stored in adistribution server is not limited specifically as long as it allows theterminal device to download and install the program from thedistribution server so that the program is executed. In addition, theprogram may be divided into multiple sections and integrated back in aterminal device after the sections are downloaded at different times, ordistribution servers for each divided section may be different.Furthermore, “computer readable recording media” includes a medium forretaining the program for a certain duration such as volatile memory(RAM) inside a computer system that becomes a server or a client whenthe program is transmitted through networks. In addition, the aboveprogram may be intended to implement part of the functions describedabove. Alternatively, the above program may be a so-called differentialfile (differential program) for implementing the above functions incombination with another program already installed in the computersystem.

Also, some or all of the above functions may be implemented as anintegrated circuit such as LSI (large scale integration). The functionsmay be set individually in separate processors. Some or all of the abovefunctions may be integrated and set in a processor. To integrate thefunctions, LSIs, or exclusive or generic processors may be used. Also,when new integration technology is made available to replace LSIsbecause of semiconductor technological development, integrated circuitsby such technology may also be applied.

INDUSTRIAL APPLICABILITY

As described above, the golf equipment fitting system and golf equipmentfitting program related to the present invention are capable of fittinggolf equipment according to the desires, skills and habits of a golfer.

DESCRIPTION OF NUMERICAL REFERENCES

1 . . . golf club, 11 . . . sensor, 12 . . . transmitter, 2 . . . golfshaft fitting system, 20 . . . receiver unit, 21 . . . swing dataacquisition unit, 221 . . . swing response surface computation unit, 222. . . time response surface computation unit, 23 . . . simulation unit,24 . . . results output unit

1. A golf equipment fitting system, comprising: a swing data acquisitionunit that acquires swing data from a sensor attached to a plurality ofgolf clubs with different specifications; a swing response surfacecomputation unit that calculates a swing response surface using theresponse surface methodology based on the swing data obtained by theswing data acquisition unit; a time response surface computation unitthat calculates a time response surface using the response surfacemethodology based on the swing data obtained by the swing dataacquisition unit; a simulation unit that calculates the swing data of agolf club that is not used for measurement from the swing responsesurface and the time response surface and simulates the swing of thegolf club based on the obtained swing data; and a results output unitthat outputs the results of simulations conducted by the simulationunit.
 2. The golf equipment fitting system according to claim 1, whereinthe specifications of a plurality of golf clubs to be used insimulations include at least the weight of a shaft.
 3. The golfequipment fitting system according to claim 1, wherein thespecifications of a plurality of golf clubs to be used in simulationsinclude at least the length of a club.
 4. The golf equipment fittingsystem according to claim 1, wherein the specifications of a pluralityof golf clubs to be used in simulations include at least two differentspecifications, and the difference in impact degrees of the twodifferent specifications is within a predetermined value.
 5. The golfequipment fitting system according to claim 1, wherein thespecifications of a plurality of golf clubs to be used in simulationsare nine specifications selected from among 27 specifications obtainedin combination of three different specifications and three levels eachof the three specifications based on an L9 orthogonal array for thedesign of experiments.
 6. The golf equipment fitting system according toclaim 5, wherein the three different specifications are shaft weight,kick point and flex.
 7. The golf equipment fitting system according toclaim 1, wherein the three different specifications are selected fromamong the stiffness, length, total weight and balance of a club.
 8. Thegolf equipment fitting system according to claim 1, wherein the threedifferent specifications are selected from among the height, depth,distance and angle of the center of gravity of the head.
 9. The golfequipment fitting system according to claim 1, wherein the threedifferent specifications are the loft angle, lie angle and face angle ofa club head.
 10. The golf equipment fitting system according to claim 5,wherein when the three different specifications are divided into theirrespective levels and when the number of levels of a first specificationis set as (i) and one level as (l), the number of levels of a secondspecification is set as (j) and one level as (m), and the number oflevels of a third specification is set as (k) and one level as (n), theresults output unit allocates a result number defined by(l−1)i+(m−1)j+(n−1)k to each of the simulation results, then, eachresult number is replaced with a plotted number, which is the valueobtained by subtracting (j−1)×k×(l−1) from the result number, andfinally the results output unit outputs data as the fitting results byentering the plotted numbers on the horizontal axis and the simulationresults on the vertical axis.
 11. The golf equipment fitting systemaccording to claim 10, wherein the results output unit outputs thefitting results as line segments by connecting the plotted dataapplicable to the following conditions (i)˜(iii): (i) data in which afirst specification is different from second and third specificationswhile second and third specifications are the same; (ii) data in which asecond specification is different from first and third specificationswhile first and third specifications are the same; and (iii) data inwhich a third specification is different from first and secondspecifications while first and second specifications are the same. 12.The golf equipment fitting system according to claim 10, wherein theresults output unit outputs fitting results by converting the results toa natural language in association with corresponding absolute values andinclinations.
 13. The golf equipment fitting system according to claim1, wherein the results output unit outputs a specification that exhibitsthe maximum value in simulation results by converting the specificationto a product name.
 14. The golf equipment fitting system according toclaim 1, wherein the results output unit selects and displays a golfclub based on the results of simulations conducted by the simulationunit.
 15. A non-transitory computer readable storage medium storing oneor more programs configured for execution by a computer, the one or moreprograms comprising instructions for: a swing data acquisition step toacquiring swing data by attaching a sensor to a plurality of golf clubswith different specifications; a calculating a swing response surfaceusing the response surface methodology based on the swing data; a timeresponse surface computation step to calculating a time response surfaceusing the response surface methodology based on the swing data; asimulation step to calculating the swing data of a golf club that is notused for measurement from the swing response surface and the timeresponse surface and simulating the swing of the golf club based on theobtained swing; and outputting the results of simulations.